Download Lecture 6 Force and Motion Identifying Forces Free

Lecture 6 Force and Motion
Identifying Forces
Free-body Diagram
Newton’s Second Law
We are now moving on from the study of motion to studying what causes
motion. Forces are what cause motion. Forces are something you already
know a lot about.
Let’s have a volunteer: I can exert a force on someone else as a push or pull.
Do you agree? I can also exert the same force on an inanimate object. Yes?
What if we add a rope into the equation. I can pull on a rope that someone
holds onto. Let’s ask the volunteer, what do you feel?
I exert a force on the rope. This creates a tension force in the rope and
the tension force is what pulls on the volunteer.
There are many objects that exert forces, like springs. If we get a
volunteer to hold one end of a spring and I pull on the other – the spring
stretches. We can also ask our volunteer what they experience.
The spring will pull on the person just as the person pulls on the spring. Now
let’s hang the spring up and attach a mass. The spring stretches, so we can
see that the spring is exerting a force up on the mass. If we hang the same
mass by a string, what can we say about the forces in this situation. The
string doesn’t appear to stretch, but if we took a microscope and looked at
the rope, we could see that there are actually spring-like bonds holding the
atoms in their places. So the spring stretches on a macroscopic level this is
where the force comes from, but the string stretches on a
microscopic/atomic level and that is where the force comes from in that
situation.
Now we’ll talk about something in physics called the normal force. [Place a
block in the center of the lecture table] Let’s identify the forces on this
block. Gravity…normal force. Now some of you may know that the normal
force in this case is the force of the table acting up on the block, but do you
actually have any proof that this so called “normal force” exists? [pass
around stiff spring, pen spring?]
We can all agree that when a spring compresses, a force is exerted. So if
we were to take a block and put in on a spring on this table, we could agree
that the compressed spring is exerting a force up on the block. So if we
could show that the table compressed when we put a mass on it, we would
have proof that it was exerting a force on the object.
[set up laser on table with shallow angle, have student mark reflected laser
point.] Now when I get up on the table, the mark moves because the table
has compressed a little! We’ve proven that the table compresses, so there
is a force up….the normal force actually exists!!! It’s really the compression
of the molecular bonds again (just like in the string) that matters.
So to recap:
• push or pull
• occurs at a point of contact between the object and some identifiable
agent that exerts the force
• exerted by animate or inanimate object
There’s another force we haven’t talked about yet. Slide your hand across
the top of the table, what do you feel? There is a force against the motion
of your hand. So friction acts parallel to the surface of contact and it acts
against the direction of motion.
Another force we have a lot of experience with is the force of gravity. I
drop something it falls. But where’s the contact in that situation? With a
push or pull, we require contact to transmit the force. In the case of
gravity we have a long-range force. The earth has a lot of mass, because of
this it pulls on everything around it. That means that everything close to
the earth feels a force pulling toward the center of the earth, hence
everything dropped falls down.
For your purposes, gravity will be the only long range force
to worry about. All other forces you’ll deal with this
semester will require contact. Now that we’ve spent a lot of
time identifying forces, let’s analyze a situation. If I throw
a ball up into the air what forces are involved after the ball
leaves my hand?
Force of the hand on the ball? Doesn’t that require contact? But if there’s
no upward force how is it moving up? We’ll leave this question for a later
answer.
So now that we’ve worked on identifying forces, we should think about the
laws of physics that govern those laws.
If I take a smooth ball and roll it along the track (the closest we’ll get to
frictionless motion), what would we expect to happen? It should roll forever
in the absence of friction. What would we have to do to change its motion?
Exert a force on it somehow. So in the absence of a force, the motion of
something at rest stays at rest, and the motion of something in motion stays
in motion. If the ball was stopped, I would have to exert a force on it or it
would stay at rest.
We are going to split the class in two groups and have you discover one of
these laws. You have a cart hooked to a pull scale. [Demonstrate pulling of
the cart.]
What kind of motion will keep the reading on the pull scale constant (nonzero)?
• motion with acceleration (constant velocity)
• motion without acceleration (increasing velocity)
As a group write your conclusion with a brief explanation on a separate sheet
of paper.
Then use the cart to try both types of motion.
After the experiment, write your conclusion on the paper. Did the
experiment confirm or dispel your initial conjecture? Explain.
What happened when you moved at constant velocity? The reading on the
scale should have dropped to zero. So our conclusions are:
• when you were accelerating the force was constant
• at constant velocity, zero acceleration, force is zero
At this point we should have discovered that forces are essential to motion.
We’ve uncovered the most important of newton’s laws of motion, Newton’s
Second Law.
The net force on an object is proportional to its acceleration.
We can write this in several different ways:
ΣF∝a, Fnet∝a.
There’s actually one more factor to complete this relationship to change the
proportional sign to an equal sign, we have to include mass. So the
relationship is a = Fnet/m. More force = more acceleration, but more mass
means less acceleration. This makes sense that to get the same acceleration
for a heavier object you have to exert more force. [add mass to cart, have
student pull it]
What do we mean by net force? This is where free-body diagrams are
valuable. Let’s draw a free-body diagram for an object sitting stationary on
this table.
First, we represent the object as a dot.
Then draw a coordinate system.
Finally we can draw the forces as
vectors, because a force has a
magnitude and direction.
We only draw forces that act on
the object. From this diagram we
can develop an equation reflecting
Newton’s Second Law.
y
N
force of table on object
x
F force
of earth on object
Fnet = N – F = ma
since a = 0, Fnet = 0, so N = F
So net force means you take all the forces in the x-direction or y-direction
and add them up. Now let’s try a more complicated diagram. What if we pull
the box across the table. Now we have forces in the x and y direction:
y
N
f force
of friction on object
force of table on object
T force of string on object
x
F force
of earth on object
So now we have the same equation as before in the y-direction:
(Fnet)y= N – F = may
since ay = 0, (Fnet)y= 0, so N = F
But now we have an equation to describe the x-direction:
(Fnet)x= T – f = max
but in this case ax ≠ 0
ax = (T – f)/m
If we knew the value of the tension and friction as well as the mass, we
would know what kind of acceleration to expect. But let’s check the limiting
cases. What if the tension was equal to the friction, there would be no
acceleration...does that mean that the object is sitting still?
What if the mass was really big…the acceleration would be really small!
So now that we know Newton’s Second Law, we can figure out how to solve
for the force of gravity. We already know the acceleration of gravity
(9.8 m/s2), so if we know F = ma, Fg = mg. Let’s figure out the units of force.
mg = kg •
m
=N
s2
N " Newton
!
So instead of saying “kilogram times meter per second squared” we just say
Newton, of course named in honor of Issac Newton who defined all these
laws of motion.
So, while we’re at it we should talk about mass. Mass is measured in
kilograms typically. It is an inherent property of matter, which means it
does not change if we change gravity. If I have a 10kg block and I take it to
the moon (where gravity is different), it would still be 10kg! But if I take it
to the moon and figure out it’s weight (the force of gravity on it, it would be
different). Let’s try the calculation.
First, does anyone know how the acceleration of gravity on the moon
compares to the acceleration of gravity on earth?
gmoon = gearth/5 = 9.8/5 = 2.0 m/s2
Fearth on object = (10kg)(9.8m/s2) = 98.0kg*m/s2 = 98N
Fmoon on object = (10kg)(2.0m/s2) = 20.0N
So again, the weight of the object will change (force of gravity on object),
but the mass which is an intrinsic property of the object does not change
because it depends on the object, not on the pull of the earth or moon.
Let’s do an example:
An elevator is going up at a steady speed. Draw a free body diagram and
write a statement of Newton’s Second law. Is the tension force greater
than equal to or less than the weight? Explain.
a=0
v